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cold brew vs latte - Decision Point

📅 May 3, 2026 👤 scraface

May 03, 2026

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Let common ratio be \( r \).
\( a_1 = 3 \), \( a_3 = 3r^2 = 27 \Rightarrow r^2 = 9 \Rightarrow r =...
Sum \( S_5 = 3 \frac{3^5 - 1}{3 - 1} = \frac{3(243 - 1)}{2} = \frac{3...
#### 363
Problem:** Solve for \( x \): \( \log_2(x + 3) + \log_2(x - 1) = 3 \).
Combine logs: \( \log_2((x + 3)(x - 1)) = 3 \)
So \( (x + 3)(x - 1) = 2^3 = 8 \)
Expand: \( x^2 + 2x - 3 = 8 \Rightarrow x^2 + 2x - 11 = 0 \)
Use quadratic formula: \( x = \frac{-2 \pm \sqrt{4 + 44}}{2} = \frac{-...
Since \( x > 1 \), take \( x = -1 + 2\sqrt{3} \approx -1 + 3.46 = 2.46...

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